Question

Number of waves made by Bohr electron in one complete revolution in $3^{rd}$ orbit is?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

Angular momentum of $n^{th}$ bohr orbit $=\frac{nh}{2\lambda }$

$m.v.r_n=\frac{nh}{2\lambda }$

$mv=\frac{h}{\lambda }$ (according to de Broglie)

$\left(\frac{h}{\lambda }\right)r_n=\frac{nh}{2\lambda }$

$n\lambda =2\pi r_n(n=3)$

$2\lambda =2\pi r_n$

these the circumference of $3^{rd}$ Bohr orbit equal to $3$ terms the wavelength of an electron makes this revolution around the $3^{rd}$ orbit

Hence no. of the wave $=3$

Hence, the correct option is $\text{C}$